
"""simple docstring"""





from itertools import count



def  lowerCamelCase__						(     __snake_case = 50      )				->						Union[str, Any]:


					"""simple docstring"""





					_UpperCamelCase									=    [1] * min_block_length

					for n in count(__snake_case      ):
										fill_count_functions.append(1      )

										for block_length in range(__snake_case,	n + 1      ):
															for block_start in range(n - block_length      ):
																				fill_count_functions[n] += fill_count_functions[
																				    n - block_start - block_length - 1
																				]

															fill_count_functions[n] += 1

										if fill_count_functions[n] > 1_00_00_00:
															break

					return n


if __name__ == "__main__":
				print(F"""{solution() = }""")











'''simple docstring'''



from math import pow
def        UpperCAmelCase (    A	:					int       ,		A	:					int       ,		A	:					int       ,		A	:					int       ,		A	:					int       ,		):
							if current_sum == needed_sum:
														# If the sum of the powers is equal to needed_sum, then we have a solution.
														solutions_count += 1
														return current_sum, solutions_count

							SCREAMING_SNAKE_CASE       :   Tuple         =      int(pow(A       ,		A					)					)
							if current_sum + i_to_n <= needed_sum:
														# If the sum of the powers is less than needed_sum, then continue adding powers.
														current_sum += i_to_n
														SCREAMING_SNAKE_CASE       ,SCREAMING_SNAKE_CASE       :   Dict         =      backtrack(
														    A       ,		A       ,		current_number + 1       ,		A       ,		A					)
														current_sum -= i_to_n
							if i_to_n < needed_sum:
														# If the power of i is less than needed_sum, then try with the next power.
														SCREAMING_SNAKE_CASE       ,SCREAMING_SNAKE_CASE       :   int         =      backtrack(
														    A       ,		A       ,		current_number + 1       ,		A       ,		A					)
							return current_sum, solutions_count
def        UpperCAmelCase (    A	:					int       ,		A	:					int					):
							if not (1 <= needed_sum <= 1000 and 2 <= power <= 10):
														raise ValueError(
														    '''Invalid input\n'''
														    '''needed_sum must be between 1 and 1000, power between 2 and 10.'''					)

							return backtrack(A       ,		A       ,		1       ,		0       ,		0					)[1]  # Return the solutions_count


if __name__ == "__main__":
							import doctest

							doctest.testmod()




